Geometry V19, Wendy Bowerman (4872/S) (06.02 MC)
Ellis is painting wooden fenceposts before putting them in his yard. They are each 7 feet tall and have a diameter of 1 foot. There are 11 fenceposts in all. How much
paint will Ellis need to paint all the surfaces of the 11 fenceposts? Use 3 14 for Pie, and round your answer to the nearest hundredth. Provide an explanation and proof
for your answer to receive full credit

9514 1404 393

  259.05 square feet

Step-by-step explanation:

The surface area of a cylinder is given by the formula ...

  SA = 2πr² +2πrh

This can be factored as ...

  SA = 2πr(r +h) . . . . . . . r is the radius, and h is the height

Here, we have a diameter of 1 ft, so the radius is 1/2 ft. Putting that and the 7 ft height into the formula, we find the area of 1 post to be ...

  SA = 2π(1/2)(1/2 +7) = 7.5π

Then the area of 11 posts will be ...

  11 · SA = 11(7.5π) = 82.5π . . . . square feet.

Using 3.14 for π, the total area of the 11 fence posts is ...

  82.5·3.14 = 259.05 . . . . square feet

Enough paint is required to cover 259.05 square feet.